$\dfrac{ -9d - 9e }{ -6 } = \dfrac{ d - 4f }{ 2 }$ Solve for $d$.
Multiply both sides by the left denominator. $\dfrac{ -9d - 9e }{ -{6} } = \dfrac{ d - 4f }{ 2 }$ $-{6} \cdot \dfrac{ -9d - 9e }{ -{6} } = -{6} \cdot \dfrac{ d - 4f }{ 2 }$ $-9d - 9e = -{6} \cdot \dfrac { d - 4f }{ 2 }$ Reduce the right side. $-9d - 9e = -{6} \cdot \dfrac{ d - 4f }{ {2} }$ $-9d - 9e = -{3} \cdot \left( d - 4f \right)$ Distribute the right side $-9d - 9e = -{3} \cdot \left( {d} - {4f} \right)$ $-9d - 9e = -{3}d + {12}f$ Combine $d$ terms on the left. $-{9d} - 9e = -{3d} + 12f$ $-{6d} - 9e = 12f$ Move the $e$ term to the right. $-6d - {9e} = 12f$ $-6d = 12f + {9e}$ Isolate $d$ by dividing both sides by its coefficient. $-{6}d = 12f + 9e$ $d = \dfrac{ 12f + 9e }{ -{6} }$ All of these terms are divisible by $3$ Divide by the common factor and swap signs so the denominator isn't negative. $d = \dfrac{ -{4}f - {3}e }{ {2} }$